Mathematical Laboratory

Code:

M1025

Acronym:

M1025

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	84	Official Study Plan	1	-	3	28	81

Teaching language

Portuguese

Objectives

Use of an algebraic manipulation program (Maxima) to treat analysis problems, algebra and geometry. Particular attention is given to the consolidation, through the development and analysis of algorithms and geometric interpretation, of the concepts and problems covered in the courses Linear Algebra and Analytic Geometry I (M1010), Real Analysis I (M1011) and topics of Elementary Mathematics (M1024).

 

Learning outcomes and competences

It is intended that at the end of the course, the student is capable of using a manipulation algebraic language (Maxima), dealing with problem of analysis, algebra and geometry, solving them, graphing and interpreting their solutions.

 

Working method

Presencial

Program

Introduction to Maxima:graphic interface; variables; functions; programming structure; graphic sketch.

Real functions of a real variable: sketch of the graph and interpretation; definition of the derivative function,  tangent line of a curve at a point; calculation and geometric interpretation of limits; integral calculus and geometric interpretation; determination of maximum and minimum of functions. Limits of sequences. Approximate calculation of series sums. Polynomial approximation of functions.

Systems of linear equations: numerical resolution, graphical representation and interpretation of the solution; implementation in Maxima of  Gauss Elimination Method and geometric interpretation. Spaces and vector subspaces: geometric representation and interpretation of linear combinations, subspaces generated by linear combinations of elements of a set, the sum of linear subspaces, bases. Linear maps: representation of the images of R2 and R3 subsets; calculation and geometric interpretation of the determinant and properties of a matrix of a linear application. Calculation and geometric interpretation of the internal product and norm of vectors, and the vector product in RR^3.

Mandatory literature

F. J. Moreira;; Apontamentos de apoio ao Maxima, 2015/16
http://maxima.sourceforge.net/documentation.html; Documentação do Software Maxima, Website, 2012
M.J. Costa; Slides de Laboratório de Matemática, M1025
M.F. Carvalho; Slides de Análise Real I M1011
M.G.Chaves; Slides de Álgebra Linear e Geometria Analítica I M1010

Complementary Bibliography

Adams Robert A.; Calculus. ISBN: 0-321-27000-2
Bauldry William C.; Linear algebra with Maple. ISBN: 0-471-06368-1
Zachary Hannan;; wxMaxima for Calculus I ; (free download at https://wxmaximafor.wordpress.com)
Zachary Hannan;; wxMaxima for Calculus II ; (free download at https://wxmaximafor.wordpress.com)

Teaching methods and learning activities

Laboratory classes: resolution by students of exercises proposed in exercise sheets and / or proposed in class. Providing of slides for support in class; in particular to support Maxima and solving some of the exercises. Support students in clarifying questions on the content and/or problem solving.

Software

Maxima

keywords

Physical sciences > Mathematics

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	53,00
Frequência das aulas	28,00
Total:	81,00

Eligibility for exams

No restrictions.

Calculation formula of final grade

The approval of the discipline can be obtained
1) by performing two tests. In this case, it is mandatory to obtain a minimum score of 7 points in each of them and the average (see calculation of final classification) of the marks obtained in the two frequencies must be  greater than or equal to 10. In this case, the student's final grade is: 0.5x (T1 + T2) where, T1 = first test score and T2 = second test score.

Each test may include resolution in computer, with a written or oral component. The second test necessarily has a component to be held on computer.

Only students who have obtained a score of 7 or higher in the 1st test can take the 2nd test.

2) by final exam (normal time or resource).

The final exam will necessarily include a test to be held in computer and may contain a written or oral  component.

Students who have passed the course for the tests and have not obtained the desired result can take the normal period exam. In this case, students will have to choose, at the time of delivery of the exam, to do away with the classification already obtained in the evaluation by tests (indicating in the exam the desired option).
 

Students with a score greater than or equal to 17.5 values may have to perform a work in Maxima or a test computer with a written or oral component or to obtain a score greater than or equal to 18 values (both in the continuous assessment,  final exam assessment and any type of special evaluation).

Examinations or Special Assignments

The exams required under special conditions will consist of a computer test with a written or oral component which can be preceded by an oral or writen or computer eliminatory exam.

 

Special assessment (TE, DA, ...)

The exams required under special conditions will consist of a computer test with a written or oral component which can be preceded by an oral eliminatory exam.